Determine how many solutions exist for the system of equations. ${8x-2y = -16}$ ${-4x-y = -3}$
Answer: Convert both equations to slope-intercept form: ${8x-2y = -16}$ $8x{-8x} - 2y = -16{-8x}$ $-2y = -16-8x$ $y = 8+4x$ ${y = 4x+8}$ ${-4x-y = -3}$ $-4x{+4x} - y = -3{+4x}$ $-y = -3+4x$ $y = 3-4x$ ${y = -4x+3}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = 4x+8}$ ${y = -4x+3}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.